The so-called magnesium support type catalytic component for the polymerization of olefins, obtained by contacting a transition metal compound such as titaniium compound with a magnesium compound, has been known.
The inventors have proposed a catalytic component which is obtained by contacting metallic magnesium, a halogenated hydrocarbon and a compound represented by the general formula X.sub.n M(OR).sub.m-n to obtain a magnesium-containing solid and contacting the magnesium-containing solid with a halogen-containing alcohol and then with a titanium compound (Japanese Patent Laid-Open Publication No. 162703/1988). This catalytic component exhibits a high catalytic activity, but forms a polymer containing somewhat more low molecular weight components, causing a problem that fuming takes place during processing the polymer. Thus, as occasion demands, it is required to remove the low molecular weight components in the polymer before processing.